Piecewise Linear Maps — Exact Chaos

Piecewise linear maps like the tent map T(x) = min(rx, r(1−x)) are exactly solvable — the invariant measure, Lyapunov exponent (λ = log r), and symbolic dynamics are all computable. Unlike smooth maps, the chaos is "exact" with no stable periodic windows for full-stretch cases.

2.00
0.50
2000
T(x) = min(2x, 2(1−x)) | λ = log(2) ≈ 0.693